Optical free-induction decay of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math>center in NaF

We have measured the optical dephasing time ${T}_{2}$ of the $^{1}A_{1}\ensuremath{\leftrightarrow}^{1}E$ zero-phonon transition of the ${F}_{3}^{+}$ color center in NaF by optical free-induction decay. In this way we eliminate the effect of the 54-GHz inhomogeneous broadening, and find a homogeneous linewidth of 20 \ifmmode\pm\else\textpm\fi{} 5 MHz ${T}_{2}=16\ifmmode\pm\else\textpm\fi{}4$ nsec). We have also measured a spontaneous emission lifetime of ${T}_{1}=10\ifmmode\pm\else\textpm\fi{}2$ nsec. In the range 1.5-4 K, our results are consistent with the relation ${T}_{2}=2{T}_{1}$, indicating that optical dephasing is limited by population-decay processes. This relation was even more clearly demonstrated by performing the same experiment on the $D$ lines of sodium vapor at 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$ Torr, where the effects of collisions are negligible. We find that the dephasing is again limited by radiative decay, and that ${T}_{2}(32\ifmmode\pm\else\textpm\fi{}3 \mathrm{nsec})=2{T}_{1}(16.3\ifmmode\pm\else\textpm\fi{}0.4 \mathrm{nsec})$.

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